| Title:
|
Mersenne numbers as a difference of two Lucas numbers (English) |
| Author:
|
Alan, Murat |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
63 |
| Issue:
|
3 |
| Year:
|
2022 |
| Pages:
|
269-276 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $(L_n)_{n\geq 0}$ be the Lucas sequence. We show that the Diophantine equation $ L_n-L_m=M_k$ has only the nonnegative integer solutions $(n,m,k)= (2,0,1)$, $(3, 1, 2)$, $(3, 2, 1)$, $(4, 3, 2)$, $(5, 3, 3)$, $(6, 2, 4)$, $(6, 5, 3)$ where $ M_k=2^k-1 $ is the $k$th Mersenne number and $ n > m$. (English) |
| Keyword:
|
Lucas number |
| Keyword:
|
Mersenne number |
| Keyword:
|
Diophantine equation |
| Keyword:
|
linear forms in logarithm |
| MSC:
|
11B39 |
| MSC:
|
11D61 |
| MSC:
|
11J86 |
| idZBL:
|
Zbl 07655799 |
| idMR:
|
MR4542788 |
| DOI:
|
10.14712/1213-7243.2022.027 |
| . |
| Date available:
|
2023-02-01T12:00:20Z |
| Last updated:
|
2024-10-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151474 |
| . |
| Reference:
|
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| Reference:
|
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| . |
